We shall gist one more example respecting squares :— Suppitse we have a square pavement, composed of equal alternate pieces of black and white marble ; the total number of small pieces to be 144, and each of them 1 foot square, as— Here there will be six black and six white pieces on each side of the square. Suppose the spectator to stand opposite the middle of the third square on the left, and that, for greater clearness, the scale be two-tenths of au iiieh to a foot, with the eye 5 feet above the ground, but at the distance of 18 feet, as before. Draw a base line r k, and divide a part of it into as many equal divisions as there are squares on one side of the original, as 1, 2. 3, 4, &c. These divisions, by the scale now adopted, will each be two-tenths of au inch. Draw the horizontal line at the distance of 5 feet (according to the scale) from the base. From the middle of the space between 2 and 3, raise a perpendicular, and to the point c, in which it cuts the horizontal line, draw lines from the commencement and the termination of the divisions on the grouteLliDe, viz., r c and 12 e. From c, set oat the distance c a, 16 feet, for the distance of the eye. Draw the line r a; and than e, where it intersects the line 12 c, draw a line, e f, parallel with the base-liue r k; will r je 12, give the boundaries of the pavement. To obtain the reticulations, draw lines from each of the divisions, 1, '2, 3, &c., on the base.line, to the centre of the picture c, and from each of the same divisions to the point of the distance D. The lines drawn from the divisions to c, from the right and left sides of the small squares, and the lines draw n front the divisions to », give the points on the line c 12, from which the horizontal lines may be drawn to form the other sides of the squares. Or, after all the lines are drawn from the divisions on the ground-line to the centre c, and also the line r n, the remain ing sides of the squares may be obtained by drawing parallel lines through the various points in which the part r e, of the line r D, intersects the lines drawn to the centre c.
It is often thought by those who are commenciug this study, that representations such as the one now given, have no resemblance to the originals ; but if they be examined, as every picture ought to be examined, Opposite to the point of sight, and at the distance for which they are drawn, the idea of their incorrectness will disappear ; to render the illusion the more complete, the figure should be viewed through at small tube or aperture, to prevent the intrusion of surround ing objects. It must also be observed, that diagrams upon paper have frequently, for the sake of convenience, a vanish ing point so near, that the eye has not the power of vision at the distance for which they are drawn. Such designs, therefore, although correct in principle, will not ap pear correct to the eye unless enlarged.
To put a circle into perspertive.—•he perspective or ob lique view of a circle, is an ellipse, and it is usually obtained by drawing a square of a size just sufficient to contain the circle, and dividing it into small circles, then putting the divided square into the perspective, and drawing within it a line through the corresponding parts of the small squares, and this line will be an ellipse. Thus, to obtain tho perspective of a circle E lig. 8, draw round it the square A B c D. Divide the square into small squares, the
number of which should be increased in proportion to the exactness with which the perspective curve must be obtained ; draw also the diagonals, c tt and A D. Throw the square and reticulations into perspective, as represented in fig. 9, IA here c is the centre of the picture, and D the point of distance ; then draw the curve by hand through the parts corresponding to those through which the circle passes in fig. S. The perspective view of a circle will be an ellipse, m [tether the square opposite the middle of one of its sides, as in lig. 9; or even with one of its angles, as in fig. 10, where a C is the line of sight ; or at a distance on one side, as in fig. 11, where 1. c is the line of sight. The point of distance, in figs. 10 and 11, is the same as in fig. 9, though in fig. 11 it could not be drawn without extending beyond the limits of the plate.
To put a triangubrr prism into perspective.—To represent in perspective a triangular prism or solid, standing vertically upon one of its ends, and viewed by an eye just opposite one of its angles; draw by admeasnrement a plan of a prism, as a t c, fig. 12 ; then draw the line a s across the outermost boundary of the triangle, and make E F parallel with o K. From e let HI the line e d, perpendicular to a K. On c d set off the measured distance of the eye from the prism, and mark the place of the eye at d. From a and b, draw lines meeting each other in d. From d, draw the line d in pa rallel with a c of the triangle., and on the other side of the line d / parallel with b c. From e raise the perpendicular ef to the measured height of the nearest angle of the prism to which the eye is opposite. On e f, measure the height of the eye from the ground-line a x, and draw the horizontal n. Take the distance c at, set it off on each side from a, and it will give the vanishing points v p and v. Draw the lines e v e and c v. Then from o and p, where the lines from a and b, iii proceeding to the eye, cut the line E F, draw the lines p q and o s, parallel with e f Draw the lines v xf, and f w T p, and the perspective outlines wfxre z, of the prism, whose base is equal to the triangle a b c, will be ob tained, and may be finished by shading it according to the direction in which the light fidls upon it. This mode of drawing from a ground-plan is extremely useful, and well calculated to show the difference between the visual and real dimensions of objects. The outlines of the house A ft c D, in lig. 2, were obtained by it ; it should be rendered familiar by frequent practice on figures in different positions.
To put a cube and cylinder into perspective.—As the base of a cube is a square, it may, when viewed as in the present example, opposite one of the angles, be put into perspective by the same process as the square in lig. 13, and figs. 9, 10, and 11, will explain the 111111111er in which the perspective of a square, seen iii other positions, may be obtained. having then obtained the base, we shall find that when n is the horizontal line, P D the points of distance, and a b half thy measured length of the diagonal of the cube, the perspective of the base will he represented by a/el g. Make the height of a c equal to the measured length according to the scale, of one of the sides of the cube, then draw the lines c D and e P.